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A factor model for joint default probabilities. Pricing of CDS, index swaps and index tranches

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  • Cantia, Catalin
  • Tunaru, Radu

Abstract

A factor model is proposed for the valuation of credit default swaps, credit indices and CDO contracts. The model of default is based on the first-passage distribution of a Brownian motion time modified by a continuous time-change. Various model specifications fall under this general approach based on defining the credit-quality process as an innovative time-change of a standard Brownian motion where the volatility process is mean reverting Lévy driven OU type process. Our models are bottom-up and can account for sudden moves in the level of CDS spreads representing the so-called credit gap risk. We develop FFT computational tools for calculating the distribution of losses and we show how to apply them to several specifications of the time-changed Brownian motion. Our line of modelling is flexible enough to facilitate the derivation of analytical formulae for conditional probabilities of default and prices of credit derivatives.

Suggested Citation

  • Cantia, Catalin & Tunaru, Radu, 2017. "A factor model for joint default probabilities. Pricing of CDS, index swaps and index tranches," Insurance: Mathematics and Economics, Elsevier, vol. 72(C), pages 21-35.
    • Handle: RePEc:eee:insuma:v:72:y:2017:i:c:p:21-35
    DOI: 10.1016/j.insmatheco.2016.10.004
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    2. Tang, Qihe & Tong, Zhiwei & Yang, Yang, 2021. "Large portfolio losses in a turbulent market," European Journal of Operational Research, Elsevier, vol. 292(2), pages 755-769.

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    More about this item

    Keywords

    Time-change; Mean-reverting process with jumps; CDS pricing; Credit index pricing; Tranche pricing;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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